Wave-transmission system



Sept. 13, 1927. 2,506

E. L. NORTON WAVE TRANSMISSION SYSTEM Filed Sept. 23. 1926 7 ///2/3 Z2 f f v f A //7ve/7/0/:'

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.UNlTEDi-STATES PATENT, OFFICE.

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WAVE-TRANSMISSION SYSTEM.

Application filed September 28,1886. Serial No. 191,270.

This invention relates to wave transmission systems, and particularl to homogeneous systems for simulating t e wave transmission characteristics of composite systems i and more particularly'to electrical networks a for simulating electromechanical systems.

An object of this invention is to simulate the wave transmission properties of a composite system, such as an electromechanical Im 1 system, by means of a homogeneous system,

such as an electrical or a mechanical system. Other objects of this invention are to bal ance the impedance of a composite electromechanical system by means of an electrical l network andto embody a composite electromechanical system in an electrical network requiring a definite relation between the 1mpedance'of its parts.

For many purposes, it is desirable to construct a homogeneous system which will simulate the wave transmission characteristics of a composite system, particularly an electrical network which will possess the same wave transmission properties as a composite electromechanical system. For example, it may be desirable, in order to determine by electrical'tests the reactions in a composite electromechanical system which may be expected under various operating conditions,

a to use a composite system for balancing the impedance of a composite system or to electrically simulate a composite system in order the mechanical veloclty' in a composite system.--

' 'In the description of this invention it should be borne in mind thatthe characteristics of wave motion in electrical and me-.

chanical systems are analogous, so that the same equations of motion apply to both systems exce t for the symbols employed. The correspon 'ng (ipantities in the two system together with t e symbols are: 1

Mechanical. Electrical.

Force =F (dynes) Voltage =E (volts) Velocity =V (cm.lsec.) Current =1 amlperes) Displacement=s (cm), Charge 00 ombs) pedance =Z (dyne sec/cm.) Impedance= (ohms) Resistance =r (dyne sec/cm. Resistance =R (ohms) l Reactanee =2: (dyne sec/cm. Reactance =X (ohms) ass =m (gms.) Inductanoe=L (henries) Compliance" =0 (cm. dyne) Capacity =C (farads) Thus, in a homogeneous system, for simulating a composite system we would expect mechanical forces to be represented by electrical voltages, mechanical velocities by electrical currents, mass elements by inductance elements, compliance elements by capacity elements, etc. Such an ordinar ty e of simulation appears to be impossib e o achieve- I ment because of the nature of the e nations relating the electrical current to t e mechanical velocity.

Nevertheless, in accordance with a feature of thisinvention, it has been found possible to obtain a peculiar type of simulation 'inwhich the wave transmission characteristics in one portion of a homogeneous system are inversely related to Wave transmission characteristics of one. side of the composite system in a similar manner to the wave transmission characteristics of inverse electrical networksyas fully discussed by O. J. Zobel and KL S. Johnson in the publications referred to in'the detaileddescript-ion which follows. In inverse networks each element or group of elements of one network is related in arrangement and composition to that of another in such away that it represents an admittance -for the impedance of the other. Thus in one network of a pair of inverse networks, a voltage resulting from a constant current excitation corresponds to a cur-. rent of the other resulting from a constant voltage excitation.

This peculiar type of simulation, in which mechamcal forces and velocities appear,'respectively, as electrical currents and electromotive forces'or vice versa, is obtained by the use of a homogeneous system having one portion composed of impedance elements equivalent to oneside of the composite system and another portion composed of impedonce elements arranged in inverse form to the elements of the other side of the system and having coefticients related thereto by the square of the coupling factor. An electrical system of this type consists of one network equivalent to the electrical portion of the composite system and a second network which is of inverse form to the analogue of the mechanical portion of the system.

In one embodiment of this invention an electrical network of the type described above is employed for accurately balancing the impedance of a composite electromechanical system.

Another embodiment of this invention consists of a constant resistance network comprising an electromechanical system in one arm, anda complementary electrical networlr designed in accordance with the above feature of the invention in another arm.

This invention can be more readily understood by reference to the following detailed description in connection with the drawings in which:

Fig. 1 shows diagrammatically the electrical analogue of a general composite electromechanical system;

Fig. shows diagrammatically a specific composite system;

Fig. 3 shows an electrical system having transmission properties equivalent to those of the composite system of Fig. 2, in accordance with the features of this invention;

Fi 4 shows an embodiment of this invention in a system for balancing the impedance of an electromagnetic system;

Fig. 5 shows the electrical analogue of the electromagnetic system of Fig. 4;

Fig. 6 showsan embodiment of this invention in which an electromagnetic system is combined in an electrical circuit employing inverse networks; and

Fig. 7 shows a simple electrical network equivalent to the composite electromechanical system of Fig.6.

Since it is now the practice to apply electrical theory and the equations for electrical wave transmission to the design of mechanical systems it is customary to represent the latter by their electrical analogues. Fig. 1 shows such an analogue of a composite electromechanical system in which E represents a source of electromotive force, Z represents the total impedance of the electrical system, P represents the coupling impedance between the electrical and mechanical systems, and Z, represents the total impedance of the mechamcal portion of the system.

The current I in the electrical system and the velocity V, in the mechanical system are related by the 'following equations, a derivation of which, from the general Lagrangian equations of motion, is given by R. L. Wegel penance in Theory of magneto-mechanical systems as applied to telephone receivers and similar structures, Journal of the American Institute of Electrical Engineers, Vol. XL, No. 10, October 1921:

1 1l e 1 i i where P, which is a constant, is the electromagnetic coupling impedance between the two systems; that is, the force factor relating the mechanical force produced to the current which produces it.

If the factor P had the same sign in both equations, it would be like an electrical mutual impedance and the composite system could be represented by a pair of trans former coupled networks in which mechanical velocities would appear as electrical currents and mechanical forces as electromotive forces. However, since the factor P has a different sign in each equation, such an equivalence appears impossible of achievement. -Nevertheless, in accordance with a feature of this invention it has been found possible to obtain an interesting and. highly useful type of equivalence in which the me chanical velocities, instead of appearing as currents, appear as electromotive forces and mechanical forces appear as currents.

This type of equivalence is obtained by connecting in series with a network representing the electrical network, a second electrical network which is of the inverse form to the mechanical portion of the system and the coefficients of the elements of which are related to the coefficients of the mechanical elements by the factor F. Such a network is the inverse of the electrical analogue of the mechanical system, the two being analogous to inverse electrical networks, such as are described in the copendin application of O. J. Zobel, Serial No. 580, 69. filed August 9, 1922 and in chapter XVIII of Transmission Circuits for'Telephonic Communication by K. S. Johnson, Van Nostrand and Company, New York.

As defined in these references, an inverse network is one so related to another network in arrangement and composition that it represents an admittance for the impedance of each element and group of elements of the other network, the ratio of the admittance to the impedance in each case (or the product of the two impedanccs) being, a constant. In the inverse network, series connections in the analo ue of the mechanical system are replaced by parallel connections and vice versa, mechanical masses are replaced by capacities, and mechanical compliances are replaced by inductances.

The proof that a homogeneous system so Hill constructed. is the equivalent of the coming the coupled mechanical elements locity and electromotive force and between force and current being, of course, a limitation) is as follows:

1 Solving equation (2) for V, we get Substituting this value for V in equation (1); and transposing we get:

It is evident from 'uatio'n (4) that the efiect of the coupled m dhanical system upon the electrical circuit is to add an impedance;

Since this expression defined a pair of inverse networks, the network constituting Z is a network of inverse form to the network constituting the impedance Z, and may be desi ed from a knowledge of the composition of that mechanical network by the rules governing the construction of inverse networks, given above.-

It follows directly from equation (4) that the voltage E across the impedance Z is equal to: t

and therefore, substituting from equation (3),

Eir= 2- also from equation v(3),

' Iy or, (9) a where F is the force in the mechanical "sys tem. These equations; (8)-and (10), show that the-voltages and currents in the electrical analogue correspond respectively to the velocity and force of the mechanical system, the form factor P appearing the same 'way the impedance ratio of a transformer appears in the equations-for coupled circuits. I g

In the foregoing analysis only Impedance has been taken into account. If the mechanical ortionof the composite system is an exten ed network, such as a mechanical filter, with some kind of a load connected to its output "terminals it is also necessary that the propagation constant of the inverse network, Z' should be equal to the propagation constant of the mechanical portion. 7

Insuch a system Z would be the input impedance of the mechanical portion.

The propagatiomand image transfer constants of themechanical network are determined from the open circuit and short circuit impedances measured at the input terminals. a

in which 9, is the transfer constant and Z and Z are, respectively, the short circuit and open. circuit impedances of the mechanical system.

Similarly,

tanh 9 in which 9 Z and Z are respectively I the transfer constant, the short circuit impedance and the open circuit impedance of the network Z The short circuit impedance of a network is. proportional to the open circuit imped-' ance of its inverse network and vice Versa, as may be seen by reference to page 90 of Transmission Circuits for Telephonic Communioatlon, to

above. Thus:

. P: v Ms= (13) and I I I i P Mo T Substituting the values from equations (13) and (14) in equation (12)- we get,

Froxiigwhich, by equation (11), i o

I tanh 9 tanh 9,

Therefore sincethe transfer constants of which reference was made the networks Z and Z are equal, and since the input voltage of the network Z corresponds to the input velocity of the mechanical network Z there will be asimilar relation between the voltages and velocities at all corresponding points in the two systems.

" Now referring to the specific composite system shown.diagrammaticallyin Fig. 2,

till

in which a source oil electronaotive torce ll; is shown connected to the Winding; ll of an electromagnetic device comprising an arms.- turc lit retained hy a spring 13, the ZHIIQB. ture and spring; are in ettect a mass m and a compliance 0 in series. lln the inverse netivorlrs at the equivalent hoinogjreneous system, the series connection becomes a parallel connection the mass hecoines a capacity and the compliance liccoines an inductance The electrical equivalent oi the composite system oil Fig. is therefore shown in 3 in which the Li ductancc l-Ll represents the winding it and r equivalent to the importance ot the electrical portion oil the svstein,

the capacity flti a value and the inthe latter two the mechaniin parallel h cal portion i 'll his may no thus:

stator system i: m and c cover the mechanical portion oi. it is equivalent to a mass,

aznce c in series so thah caiostiruti.

l lationaliw a ally lel circuit E0113 eonchnascii' at l ipgs. l and ti tions at this invei. .r

l r. sho system employing the equivalent netivorlr out this invention :tor halancing the impedance oil an electromagnetic receiver. This s cm comprises two siqnalinp; lines 10 and Oil Ell between which it it. desired to prevent interaction While perinittinp; two-Way communication between each and an operators $13 finch arrangement :lor trample, might be advantageous tor use a monitoring" circuit tor telephone lines equipped with repeaters. The telephone comprises a transmitter M connected in series with a battery to the primary oi": a transitornier 526 the secondarv of which is connected in series with the windings of an electromagnetic receiver 27. The halanced operating; ar angement is obtained by use oil a livbrld coil 28 and a network 29 tor balancing the impedance of the telephone set. The network 29 comprises a series connection oil a transformer 30, having a resistance 36 connected to its secondary winding tor balancing the i111- pedance oi the transiformer 26 and the transmitter 52 i, and a network 3i, for balancing the impedance oi. the receiver 27. its ere plained in detail in the following paragraph, the netivorlr 3? is constructed in accordance with the principles oi this invention set :torth ahove. 'lhis operates so that waves from either of the lines 520 or 21 divide hetwecn the set 523 and the network 29 but are not transmitted to the other line, While sip;- naling Waves generated lrv the transmitter fl t are effective in hoth oil the lines 20 and ill.

l io; 5 shows the electrical analogue ot the receiver Ell' in which l1 represents the inductance ot the windings 2th l represents the coupling}; impedance hetivcen the elcctrical. and mechanical portions of the system TIL: and. c reprcseuh rcapcctivclv the mass and compliance oi. the diaphragm 513i),

c represents the compliance o the air chain her 33. and m represents the resistance oi? the aperture 3 1;, .lhe netivor t 3i", which is constructed in accordance with the this invention tor simulating the impedance characteristics oil the receiver Q7, comprises an inductance having; a value lL- tor simulating: the ire ieclance of the windings 31 connected in series with. an inverse network 'lor simulating; the mechanical portion of the receiver: The inverse netvvorlr comprises a shunt inductance oi a value c ll, a shunt aeitv tlll cl tauce ll cit value c l and a terminating inc it resist l] in". (5 shows constant resistance netivorlr cinhodvingr an electroi'naa etic device and a netivorlr according; to this invention. thipposing, ior example it is desired to introduce a receiver between the two sets oi. terminals principles or" ill!) a series induc aw t it) and t5, it. the latter of which are connected to a circuit having a constant resistance impedance Without adding rariahle importance the circuit. As set torth in the application at U. ill. i lobel, rcicr'rccl to ahove this cai'i he done hv the use ct in- WU vc e netivorlr 'lIhns. it the receiver is in sertecl in series arm the impedance at the terminals til, tat can hemaintained a conresistance lav insertina the inverse net u o l nivorlr oil the recelver in a shunt arm. Use is 125 made ot the method oil the present invention tor ohtainin r a homogeneous system equivalent to a, composite system in order to con street the inverse netvvorh or the receiver.

Thus a loud speaking receiver 47 shunted by we 55 second part having an impedance inversea resistance element 48of value R is connected in a series arm, while there is connected in a shunt arm a network 49 having The network 49 is designed as follows:

. -The electrical-analogue of the loud speaking receiver 47 is identical in arrangement of elements to the analogue shown in Fig. 5 of the receiver 27 of Fig. 4. For receiver 47,

' L represents the inductance of the windings .51, 1 represents the coupling impedance between the electrical and mechanical portions,

0', and m represent;respectively, the compliance andmass ofthediaphragm- 52, a,

represents the compliance of the air chamber l 65, condenserjfifi,

53, and- Ir", represents the resistance of the horn. 54. 1 The receiver-can therefore'be represented by the electrical network of Fig.

7 in which inductance element 58 has a value L inductance element 59, a value 0 1 condenser 60, a valuef; inductance element 61, a value c P and resistance 62, a

l value 5* The network 49 must therefore 4. be constructed to be the inverse form of this network, the condenser 63 having a value mgR at; inductance element 64.

2 and resistance It should be noted that since in the network 49 the inverse transformation is twice made,the impedance elements related to the mechanical portion of the. composite system appear in the same arrangement as they do in the electrical analogue altho ugh ghey d1ffor in value by the ratio or m the masses (inductances) and resistances or the compliances' (capacities), respectively.

What is claimed is:

1. A homogeneous wave transmission sys-' tem for simulating the wave transmission characteristics of a composite wave transmissionsyst-em having an electrical portion and mechanical portion, said homogeneous system comprisingv one part having an impedance equal to the impedance of one portion of the composite system and a ly proportional to the impedance of the other POI'tlOIlyOf the composite system.

2. A homog'eneouswave transmission sys- .-.tem for simulating the wave transmission characteristics of a composite system having an" electrical-portion and a mechanical port-ion so coupled as to transmit wave'en- 'ergy from one to the other, said homogeneous system comprising one'part having an ;condenser impedance corresponding to the impedance ofone of said 1portions of the c'ompqsite sys-- tem and anot or part effectively in series "therewith and comprising impedance elements of inverse form and arrangement to the elements of the analogue of the other of said portions of the composite system, the coties appear as electromotive forces and mecha-nica forces as electrical currents and vice versa, said homogeneous system. comprising one part-composed of im edance elements corresponding to the impe ance elements of one portion of the composite s stem and another part composed of impe ance elements of inverse form and arrangement to the analogue of the other portion of the composite system, the impedance Z of said last mentioned part being related.- to the im-' pedance Z of said other portion of the composite system by the equation;

ZZ IP in which P is the coupling factorsbetween the electrical and mechanical portions of the compasite system;

4. An electrical network for simulating the wave. transmission characteristics of a com site electromechanical system having an e ectrical portion and a mechanical portion, said simulation being of such a type that mechanical velocities appear as electromotive forces and mechanical forces as electrical currents, said electrical network comprising two branches one of which is composed of impedance elements equivalent tov the im edance elements of the electrical portion 0 the composite system and the other of which is com osed of impedance elements of inverse form and arrangement to the impedance elements of the analogue of the mechanical portion of the composite system.

5. An electrical network for simulating the Wave transmission characteristics of a composite. electromechanical system having an electrical portion of impedance Z'and a mechanical portion of impedance Z where Z and Z are any functions of frequency, said net-work comprising two series connected branches one of which has an impedance equal to Z, and the other of which" 2 has. an impedanceequal to 2 where P is V 80 and an electrical portion, said simulation being of such a type that mechanical veloci menace and mechanical portions of the composite system.

.6. in combination, a composite electromechanical system comprising an electrical portion and a mechanical portion, and a homogeneous system having an impedance proportional to the impedance of said composite system, said homogeneous system com prising one portion having impedance elements of similar form and arranged in a manner similar to the impedance elements of one of said portions of the composite system, and a second portion having impedance elements of inverse form and arrangement to the impedance elements of the other ot said portions of the composite system.

7. In combination, a composite electromechanical system, comprising an electrical portion and a mechanical portion and an electrical network. having" an im edance proportional to the impedance of said composite system, said networkcomprising one branch composed of impedance elements of a similar form and arran 'ed in a manner similar to the impedance elements of one of said portions of the composite system, and a second network connected in series there with and composed of impedance elements of inverse form and arrangement to the impedance elements of the other of said portions of the composite system.

8. In combination, a composite electromechanical system, comprising an electrical portion of impedance Z, and a mechanical portion of impedance Z where Z and Z are any functions of frequency, and an electrical network for balancing the impedance of said composite system, said network comprising a circuit branch of impedance Z,,

and a second circuit branch impedance connected in series therewith, Where P is the coupling factor between the electrical and mechanical portions of i said composite system.

In witness whereof, I hereunto subscribe my name this 21st day of September, A. D. 19 6.

EDWARD L. NORTON. 

